Structural Anisotropy in Polar Fluids Subjected to Periodic Boundary Conditions.
Ontology highlight
ABSTRACT:
SUBMITTER: Stenhammar J
PROVIDER: S-EPMC3269192 | biostudies-other | 2011 Dec
REPOSITORIES: biostudies-other
Similar Datasets
Project description:Word match counts have traditionally been proposed as an alignment-free measure of similarity for biological sequences. The D(2) statistic, which simply counts the number of exact word matches between two sequences, is a useful test bed for developing rigorous mathematical results, which can then be extended to more biologically useful measures. The distributional properties of the D(2) statistic under the null hypothesis of identically and independently distributed letters have been studied extensively, but no comprehensive study of the D(2) distribution for biologically more realistic higher-order Markovian sequences exists. Here we derive exact formulas for the mean and variance of the D(2) statistic for Markovian sequences of any order, and demonstrate through Monte Carlo simulations that the entire distribution is accurately characterized by a Pólya-Aeppli distribution for sequence lengths of biological interest. The approach is novel in that Markovian dependency is defined for sequences with periodic boundary conditions, and this enables exact analytic formulas for the mean and variance to be derived. We also carry out a preliminary comparison between the approximate D(2) distribution computed with the theoretical mean and variance under a Markovian hypothesis and an empirical D(2) distribution from the human genome.
| S-EPMC3880068 | biostudies-literature
Project description:Electro-optical cell based on the cholesteric liquid crystal is studied with unique combination of the boundary conditions: conical anchoring on the one substrate and planar anchoring on another one. Periodic structures in cholesteric layer and their transformation under applied electric field are considered by polarizing optical microscopy, the experimental findings are supported by the data of the calculations performed using the extended Frank elastic continuum approach. Such structures are the set of alternating over- and under-twisted defect lines whose azimuthal director angles differ by [Formula: see text]. The [Formula: see text] and [Formula: see text]-defects of periodicity, which are the smooth transition between the defect lines, are observed at the edge of electrode area. The growth direction of defect lines forming a diffraction grating can be controlled by applying a voltage in the range of [Formula: see text] V during the process. Resulting orientation and distance between the lines don't change under voltage. However, at [Formula: see text] V [Formula: see text]-defects move along the defect lines away from the electrode edges, and, finally, the grating lines collapse at the cell's center. These results open a way for the use of such cholesteric material in applications with periodic defect structures where a periodicity, orientation, and configuration of defects should be adjusted.
| S-EPMC8052423 | biostudies-literature
Project description:The periodic Saffman-Delbrück (PSD) model, an extension of the Saffman-Delbrück model developed to describe the effects of periodic boundary conditions on the diffusion constants of lipids and proteins obtained from simulation, is tested using the coarse-grained Martini and all-atom CHARMM36 (C36) force fields. Simulations of pure Martini dipalmitoylphosphatidylcholine (DPPC) bilayers and those with one embedded gramicidin A (gA) dimer or one gA monomer with sizes ranging from 512 to 2048 lipids support the PSD model. Underestimates of D? (the value of the diffusion constant for an infinite system) from the 512-lipid system are 35% for DPPC, 45% for the gA monomer, and 70% for the gA dimer. Simulations of all-atom DPPC and dioleoylphosphatidylcholine (DOPC) bilayers yield diffusion constants not far from experiment. However, the PSD model predicts that diffusion constants at the sizes of the simulation should underestimate experiment by approximately a factor of 3 for DPPC and 2 for DOPC. This likely implies a deficiency in the C36 force field. A Bayesian method for extrapolating diffusion constants of lipids and proteins in membranes obtained from simulation to infinite system size is provided.
| S-EPMC6326097 | biostudies-literature
Project description:A theoretical methodology based on quantum chemistry to calculate mechanical properties of polymer crystals has been developed and applied to representative polymers. By density functional theory calculations including a dispersion force correction under three-dimensional periodic boundary conditions, crystal structures of poly(methylene oxide) (PMO), polyethylene (PE), poly(ethylene terephthalate) (PET), poly(trimethylene terephthalate) (PTT), and poly(butylene terephthalate) (PBT) were optimized and their mechanical properties, such as crystalline moduli and linear and volume compressibilities, were calculated. The optimized crystal structures were proved to be fully consistent with those determined by X-ray and neutron diffraction. The crystalline moduli (E ∥) parallel to the chain axis were calculated to be 114 GPa (PMO), 333 GPa (PE), 182 GPa (PET), 7.1 GPa (PTT), and 20.8 GPa (PBT) and compared with those determined from X-ray diffraction, Raman spectroscopy, and neutron inelastic scattering experiments. Herein, the E ∥ values thus determined are interpreted in terms of conformational characteristics of the polymeric chains and the validity of the homogeneous stress hypothesis adopted in the X-ray diffraction method is also discussed.
| S-EPMC6641976 | biostudies-literature
Project description:Electroosmotic flow (EOF) is widely used in microfluidic systems and chemical analysis. It is driven by an electric force inside microchannel with highly charged boundary conditions. In practical applications, electrochemical boundary conditions are often inhomogeneous because different materials as walls are commonly utilized in routine fabrication methods. In the present study, we focus on the analytic solutions of the EOF generated in a planar microchannel with asymmetric electrochemical boundary conditions for non-Newtonian fluids. The velocity profile and flow rate are approximated by employing the power-law model of fluids in the Cauchy momentum equation. The hydrodynamic features of the EOF under asymmetric zeta potentials are scrutinized as a function of the fluid behavior index of the power-law fluid, thickness of Debye length, and zeta potential ratios between planes. The approximate solutions of the power-law model are comparable to the numerically obtained solutions when the Debye length is small and the fluid behavior index is close to unity. This study provides insights into the electrical control of non-Newtonian fluids, such as biological materials of blood, saliva, and DNA solution, in lab-on-a-chip devices.
| S-EPMC6187346 | biostudies-literature
Project description:In equilibrium, disorder conspires with topological defects to redefine the ordered states of matter in systems as diverse as crystals, superconductors, and liquid crystals. Far from equilibrium, however, the consequences of quenched disorder on active condensed matter remain virtually uncharted. Here, we reveal a state of strongly disordered active matter with no counterparts in equilibrium: a dynamical vortex glass. Combining microfluidic experiments and theory, we show how colloidal flocks collectively cruise through disordered environments without relaxing the topological singularities of their flows. The resulting state is highly dynamical but the flow patterns, shaped by a finite density of frozen vortices, are stationary and exponentially degenerated. Quenched isotropic disorder acts as a random gauge field turning active liquids into dynamical vortex glasses. We argue that this robust mechanism should shape the collective dynamics of a broad class of disordered active matter, from synthetic active nematics to collections of living cells exploring heterogeneous media.
| S-EPMC7958234 | biostudies-literature
Project description:A novel hybrid FRP-aluminum truss system has been employed in a two-rut modular bridge superstructure composed of twin inverted triangular trusses. The actual flexural behavior of a one-rut truss has been previously investigated under the on-axis loading test; however, the structural performance of the one-rut truss subjected to an off-axis load is still not fully understood. In this paper, a geometrical linear finite element model is introduced and validated by the on-axis loading test; the structural performance of the one-rut truss subjected to off-axis load was numerically obtained; the dissimilarities of the structural performance between the two different loading cases are investigated in detail. The results indicated that (1) the structural behavior of the off-axis load differs from that of the on-axis load, and the off-axis load is the critical loading condition controlling the structural performance of the triangular truss; (2) under the off-axis load, the FRP trussed members and connectors bear certain out-of-plane bending moments and are subjected to a complicated stress state; and (3) the stress state of these members does not match that of the initial design, and optimization for the redesign of these members is needed, especially for the pretightened teeth connectors.
| S-EPMC4164816 | biostudies-other
Project description:The boundary-element method (BEM) is widely used for electrocardiogram (ECG) simulation. Its major disadvantage is its perceived inability to deal with the anisotropic electric conductivity of the myocardial interstitium, which led researchers to represent only intracellular anisotropy or neglect anisotropy altogether. We computed ECGs with a BEM model based on dipole sources that accounted for a "compound" anisotropy ratio. The ECGs were compared with those computed by a finite-difference model, in which intracellular and interstitial anisotropy could be represented without compromise. For a given set of conductivities, we always found a compound anisotropy value that led to acceptable differences between BEM and finite-difference results. In contrast, a fully isotropic model produced unacceptably large differences. A model that accounted only for intracellular anisotropy showed intermediate performance. We conclude that using a compound anisotropy ratio allows BEM-based ECG models to more accurately represent both anisotropies.
| S-EPMC2688616 | biostudies-other
Project description:Twin boundaries (TBs) have been observed in and introduced into nonmetallic materials in recent years, which brought new concepts for the design of new structural materials. However, the roles of TB on the mechanical properties and strengthening/softening of transition metal nitrides remain unclear. To investigate the TB effects and the in-plane anisotropy, nanoindentations on VN (111) films with and without TB were simulated with molecular dynamics, in which a cylindrical indenter was used, and its longitudinal axis were assigned along <112> and <110>, respectively. We found that the effect of the indenter orientation is insignificant in the elastic stage, but significant in the following inelastic deformation. Different deformation mechanisms can be found for inelastic deformation, such as twinning and dislocation glide. The migration of TB can be observed, which may release the internal stress, resulting in softening; while the dislocation locking and pileup at TB can enhance the strength. We also found that the strengthening/softening induced by TB depends on the deformation mechanisms induced by indenter directions.
| S-EPMC5500517 | biostudies-literature
Project description:Equations of the Loewner class subject to non-constant boundary conditions along the real axis are formulated and solved giving the geodesic paths of slits growing in the upper half complex plane. The problem is motivated by Laplacian growth in which the slits represent thin fingers growing in a diffusion field. A single finger follows a curved path determined by the forcing function appearing in Loewner's equation. This function is found by solving an ordinary differential equation whose terms depend on curvature properties of the streamlines of the diffusive field in the conformally mapped 'mathematical' plane. The effect of boundary conditions specifying either piecewise constant values of the field variable along the real axis, or a dipole placed on the real axis, reveal a range of behaviours for the growing slit. These include regions along the real axis from which no slit growth is possible, regions where paths grow to infinity, or regions where paths curve back toward the real axis terminating in finite time. Symmetric pairs of paths subject to the piecewise constant boundary condition along the real axis are also computed, demonstrating that paths which grow to infinity evolve asymptotically toward an angle of bifurcation of π/5.
| S-EPMC7655755 | biostudies-literature